15th International Conference on Fluid Control, Measurements and Visualization27-30 May, 2019, Naples, Italy

Full-field and time-resolved tomographic PIV of turbulent thermal convectioninside a cylinder

Gerardo Paolillo1,*, Carlo Salvatore Greco1, Tommaso Astarita1, Gennaro Cardone1

1Department of Industrial Engineering, University of Naples “Federico II”, Naples, Italy*corresponding author: gerardo.paolillo@unina.it

Abstract Rayleigh-Bénard convection, the buoyancy-driven flow induced by temperature gradients par-allel to the gravity, is relevant to a variety of processes spontaneously occurring in nature or used intechnological applications. Understanding of its inherent chaotic evolution is possible only through mea-surement techniques that allow to access the unsteady, three-dimensional behavior of all the thermo-fluiddynamic quantities of the flow. This work presents full-field and time-resolved tomographic particle im-age velocimetry measurements of non-rotating and rotating Rayleigh-Bénard convection inside a slendercylinder with aspect ratio equal to 1/2 at Rayleigh and Prandtl numbers equal to 1.86×108 and 7.6.Keywords: thermal convection, rotating convection, particle image velocimetry

1 Introduction

Rayleigh-Bénard (RB) convection, the buoyancy-driven flow induced by temperature gradients parallel to thegravity, plays a key role in a large number of natural processes (wind generation, oceanic circulation, convectionin the stars’ interior, etc.) and technological applications (such as turbomachinery flows, melting of pure metalsand gas separation based on centrifugation). In several contexts, a background rotation occurs to significantlychange the dynamics of the thermal convection. For instance, the interplay between the buoyancy and theCoriolis forces is at the basis of the formation of tropical hurricanes and it might even explain the genesis ofthe Earth’s magnetic field according to the geodynamo theory. Since the study of such phenomena is verycomplicated, the basic mechanisms of RB convection are typically investigated in confined, basic geometries,like rectangular or cylindrical cells [1, 2, 5]. This allows, on one side, to simplify the theoretical analysis, onthe other, to obtain comparable results from the experimental and numerical sides, since the flow boundaryconditions are easily reproducible in both cases. In particular, the cylindrical geometry is of much interest,because it has one direction of statistical homogeneity (the azimuthal one, provided that the cylinder is leveled),which prevents the existence of preferential orientations in the development of the large-scale structures of theturbulent flow.

The inherent turbulent nature of RB convection makes three-dimensional measurements mandatory for theanalysis of such a phenomenon. In this work, the time-resolved tomographic particle image velocimetry (PIV)is used to investigate the whole domain of RB convection inside a cylinder with aspect ratio equal to 1/2 atRayleigh and Prandtl numbers equal to 1.86× 108 and 7.6, respectively. The effects of rotation on the flowdynamics and evolution are also investigated in similar operating conditions by varying the Rossby number.

2 Experimental setup

The convection cell is a Plexiglas cylinder filled with water, heated from below by a flat heater coupled witha copper plate and cooled from above by means of a transparent water exchanger. Both plates are maintainedat constant temperature by means of a thermoelectric controller performing a PID control with a stability upto 0.01◦C. The flow is seeded with fluorescent orange polyethylene seeding particles illuminated by a Nd:YAGlaser shaped into a cylindrical beam, which covers the whole cylinder interior. Image particles are recorded byfour sCMOS cameras (Andor Zyla, 5.5 megapixels), arranged in an planar configuration with a constant angularspacing of 40◦. The digital resolution of the cameras is about 14 voxel/mm, while the sampling frequency is7.5 Hz. This is sufficient to obtain time-resolved measurements by virtue of the slow velocities of the thermalconvection. The duration of each experiment is 4 hours, in such a way that a reliable statistical analysis can

Extended Abstract ID:25 1

15th International Conference on Fluid Control, Measurements and Visualization27-30 May, 2019, Naples, Italy

(a) Ra = 1.86×108, Pr = 7.6, Ro = ∞ (b) Ra = 2.86×108, Pr = 6.4, Ro = 0.1

Fig. 1 Large-scale structures of RB convection in a cylinder with aspect ratio equal to 1/2 (a) without and (b) witha background rotation. Isosurfaces and slices of the vertical velocity component (instantaneous velocity field).Velocity are scaled by the free-fall velocity u0 =

√β∆T gL, where β is the volumetric expansion coefficient, ∆T

is the temperature difference across the fluid layer, g is the gravity acceleration and L is the cylinder height.

be carried out. All the equipment, except the laser, is placed on a rotating table which is operated at angularvelocities greater than 30◦/s. Time-resolved motion analysis is based on the most recent techniques for particletracking, essentially ‘Shake-the-Box’ [3] and the iterative particle reconstruction method [4].

3 Results

In agreement with previous investigations [1], in the non-rotating case the instantaneous velocity field shows theexistence of a large-scale circulation (LSC). This exhibits a chaotic behavior which can be inspected by meansof the time-resolved measurements and characterized statistically thanks to the great amount of data collected(see Fig. 1(a)). In particular, proper orthogonal decomposition allows to identify the most energetic modes ofthe thermal convection. This analysis confirms that the principal states of the LSC are the single-roll and thedouble-roll states, already observed in previous experimental and numerical investigations. It is also shown thatthe oscillatory modes of the LSC are related to the POD modes and these latter offer the possibility to definea better criterion for the identification of the LSC orientation (an aspect that attracts a lot of attention fromscientists working in the field). When rotation is added, the LSC circulation breaks down and is replaced bycolumnar vortices, which extends over the entire cell (see Fig. 1(b)). The size of such structures is observed todecrease when increasing the background rotation; correspondingly, their concentration is observed to increase.

References

[1] Ahlers G, Grossmann S, Lohse D (2009) Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection. Review of Modern Physics, vol. 81, pp. 503-507. doi: 10.1103/RevModPhys.81.503.

[2] Lohse D, Xia K Q (2010) Small-scale properties of turbulent Rayleigh-Bénard convection. Annual Reviewof Fluid Mechanics, vol. 42, pp. 335-364. doi: 10.1146/annurev.fluid.010908.165152.

[3] Schanz D, Gesemann S, Schr’́o der A (2016) Shake-The-Box: Lagrangian particle tracking at high particleimage densities. Experiments in Fluids, vol. 57, pp. 70:1-27. doi: 10.1007/s00348-016-2157-1.

[4] Wieneke B (2012) Iterative reconstruction of volumetric particle distribution. Measurement Science andTechnology, vol. 24, pp. 024008:1-14. doi: 10.1088/0957-0233/24/2/024008/meta.

[5] Xia K Q (2013) Current trends and future directions in turbulent thermal convection. Theoretical andApplied Mechanics Letters, vol. 3, pp. 052001:1-12. doi: 10.1063/2.1305201.

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